The expected value is the arithmetic mean of a large number of independently selected outcomes of a random variable.
a) No, X and Y are not independent since the lifetime of a part (Y) is modeled by X.
b) The joint PDF fX,Y(x,y) = x-1exp(-xy) for 1 ≤ x ≤ 2, y ≥ 0, 0 otherwise.
c) P[Y < 1] = 1 - exp(-x) for 1 ≤ x ≤ 2.
d) The marginal PDF fY(y) = exp(-xy) for 1 ≤ x ≤ 2, y ≥ 0, 0 otherwise.
e) The expected value of Y using fY(y) is 1/x for 1 ≤ x ≤ 2.
f) The conditional expected value of Y given X = x is 1/x for 1 ≤ x ≤ 2.
g) Using E[Y] = E[E[Y∣X]], the expected value of Y is 1.
h) The expected value of X + Y is 2.
i) The expected value of XY is 1.
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- Per the NEC® the number of receptacles required in a classroom is ____. The room
is 36 feet x 24 feet with a 3-foot wide door at the far end of one of the 36-foot long walls. Nobody
lives there!
The number of receptacles required in the classroom is 14.
What is the number of receptacles?
To determine the number of receptacles required in a classroom, we need to consider the electrical code requirements for the room size and layout.
According to the National Electrical Code (NEC), there should be at least one duplex receptacle for every 12 linear feet of wall space in a classroom.
In addition, there should be at least one receptacle within 6 feet of each doorway and at least one receptacle on each wall space that is 2 feet or more in width.
Using this information and the dimensions provided, we can calculate the required number of receptacles as follows:
Calculate the perimeter of the room:
Perimeter = 2(Length + Width) = 2(36 + 24) = 120 feet
Calculate the total linear feet of wall space:
Total wall space = Perimeter - Width of door = 120 - 3 = 117 feet
Determine the number of receptacles required:
Number of receptacles = Total wall space / 12 + Number of doorways + Number of wall spaces wider than 2 feet
Number of doorways = 1 (as stated in the question)
Number of wall spaces wider than 2 feet = 2 (the two 24-foot-long walls)
Number of receptacles = (117 / 12) + 1 + 2 = 11 + 1 + 2 = 14
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4. A polygon with area 10 square units is dilated by a scale factor of k. Find
the area of the image for each value of k. (Lesson 5-4)
a. k = 4
b. k = 1.5
c. k = 1
d. k = 1/3
Answer:
If a polygon is dilated by a scale factor of k, then its area is multiplied by k².
a. When k = 4, the area of the image is 10 × 4² = 160 square units.
b. When k = 1.5, the area of the image is 10 × 1.5² = 22.5 square units.
c. When k = 1, the area of the image is 10 × 1² = 10 square units. (The image is the same size as the original.)
d. When k = 1/3, the area of the image is 10 × (1/3)² = 10/9 square units.
Step-by-step explanation:
why can't we use mean when a data set has one or two values that are much higher than all of the others
The reason we can't use the mean when a data set has one or two values that are much higher than all of the others is that it skews the average, making it not representative of the rest of the data.
What is the mean?The mean is a numerical measure of the central tendency of a data set. It is calculated by dividing the sum of all the values in a data set by the number of data points.
A data set is a collection of observations or measurements that are analyzed to obtain information. It can be represented graphically, in tabular form, or in any other format. The data set may be a sample or the entire population.
If a data set has one or two extremely high or low values, it can significantly impact the mean. These values are known as outliers. The outliers can cause the mean to be higher or lower than the actual middle value of the data.
Hence, in such cases, the median is a better choice for finding the central tendency of the data. The median is the middle value of the data set, and it is less affected by outliers than the mean. The mode, which is the value that occurs most frequently in the data set, is also a measure of central tendency that is less sensitive to outliers than the mean.
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25 POINTS
1. Explain the process of verifying a trigonometric identity.
2. What is a similarity and difference between verifying a trigonometric identity and solving an equation?
3. How do you find the value of cos120° using the sum or difference formula?
4. How do you decide whether to use a positive or negative sign in the half- angle formula for sine and cosine?
5. When solving a trigonometric equation, what is the difference between finding all solutions and finding all solutions within a specific interval?
The process of verifying trigonometric identity involves the use of Pythagorean theorem, double angle formula etc. The similarity between verifying a trigonometric identity and solving an equation is that it both involves mathematical expressions.
What is the process of verifying a trigonometric identity?1. The process of verifying a trigonometric identity involves using various trigonometric identities and properties to manipulate one side of the equation until it is simplified to the other side. This typically involves using algebraic manipulations, such as factoring and combining like terms, as well as trigonometric identities such as the Pythagorean identity, double angle formula, or sum and difference formula.
2. One similarity between verifying a trigonometric identity and solving an equation is that both processes involve manipulating mathematical expressions. However, a key difference is that verifying a trigonometric identity requires proving that the identity holds for all values of the variables involved, whereas solving an equation involves finding the specific values of the variables that make the equation true.
3. To find the value of cos120° using the sum or difference formula, we can use the fact that 120° is equal to 60° + 60°. We can then use the cosine sum formula, which states that cos(x+y) = cos(x)cos(y) - sin(x)sin(y), with x = y = 60°. This gives us:
[tex]cos(120\°) = cos(60\° + 60\°) = cos(60\°)cos(60\°) - sin(60\°)sin(60\°) = \frac{1}{2}*\frac{1}{2} - (\sqrt(3)/2)(\sqrt(3)/2) = -1/2[/tex]
Therefore, cos120° = -1/2.
4. The sign to use in the half-angle formula for sine and cosine depends on the quadrant in which the angle lies. If the angle is in the first or second quadrant, we use the positive sign. If the angle is in the third or fourth quadrant, we use the negative sign. For example, if we want to find sin(x/2) and x lies in the third quadrant (i.e., between 180° and 270°), we use the negative sign in the formula sin(x/2) = -√((1-cos(x))/2).
5. When solving a trigonometric equation, finding all solutions means determining all possible values of the variable that make the equation true, regardless of the range of values allowed for the variable. Finding all solutions within a specific interval, on the other hand, means restricting the values of the variable to a certain range and finding all possible solutions within that range. This is important because trigonometric functions are periodic and have infinitely many solutions, so it is often necessary to specify a range of values in order to obtain a finite set of solutions.
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Create a Dataset Give a positive integer less than 100 as the last data value in each of the following datasets so that the resulting dataset satisfies the given condition (a) The mean of the numbers is substantially less than the median 51,52,53,54 (b) The mean of the numbers is substantially more than the median 2,3,4,5, (c) The mean and the median are equal. 2,3,4,5
(a) Dataset with mean substantially less than median:
9, 10, 11, 12, 90
The mean of this dataset is (9+10+11+12+90)/5 = 26.4, while the median is 11, which is substantially greater than the mean. The last data value is 90, which is a positive integer less than 100.
(b) Dataset with mean substantially more than median:
98, 99, 100, 101, 200
The mean of this dataset is (98+99+100+101+200)/5 = 119.6, while the median is 100, which is substantially less than the mean. The last data value is 200, which is a positive integer less than 100.
(c) Dataset with mean equal to median:
2, 3, 4, 4, 5
The mean of this dataset is (2+3+4+4+5)/5 = 3.6, which is equal to the median (the middle value of the dataset). The last data value is 5, which is a positive integer less than 100.
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I don't really understand how to do reference angles. I only need the last one, -60 degrees, does anyone know how to figure out it's reference angle?
Answer: 60?
Step-by-step explanation:
The reference angle is the acute angle formed between the terminal side of an angle in standard position and the x-axis. To find the reference angle of an angle, you can follow these steps:
Determine the quadrant in which the angle terminates. For -60 degrees, this would be the fourth quadrant.
Determine the corresponding angle in the first quadrant by finding the angle formed between the terminal side and the x-axis. In the fourth quadrant, this angle is equal to 360 degrees minus the original angle. So for -60 degrees, the corresponding angle in the first quadrant is 360 - 60 = 300 degrees.
Subtract this angle from 360 degrees to find the reference angle. For -60 degrees, the reference angle is 360 - 300 = 60 degrees.
Therefore, the reference angle of -60 degrees is 60 degrees.
Find X
Picture Below
Step-by-step explanation:
From CalcWorkshop:
" Intersecting Chords Theorem. If two chords or secants intersect in the interior of a circle, then the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord "
6 * 4 = 8 * x
x = 3
Two cars are driving away from an intersection in perpendicular directions. The first cars velocity isms 7 meters per second and the second cars velocity is 3 meters per second. At a certain instant, the first car is 5 meters from the intersection and the second car is 12 meters from the intersection. What is the rate of change of the distance between the cars at that instant?
The rate of change of the distance between the cars at that instant is 5.46 meters/ second.
The first car's velocity = 7 meters per second
The second car's velocity = 3 meters per second.
Distance from the intersection of first car = 5m
Distance from the intersection of second car = 12m
The rate of change is used to numerically quantify the percentage change in value over a predetermined period of time. It is a measure of a variable's velocity.
Calculating the distance between both cars at the instant
= √(12² + 5²)
= √ 144 + 25
= √169
= 13
Calculating the rate of change of distance -
2d/dt
= d(x² + y²)/dt
= 2x dx/dt + 2ydy/dt
= 2×5×7 + 2×12×3
= 70 + 72
= 142
Therefore, total distance -
dd/dt
= 142/26
= 5.46
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3.27 Underage drinking, Part 2: we learned in Exercise 3.25 that about 69.7% of 18-20 year olds consumed alcoholic beverages in 2008. We now consider a random sample of fifty 18-20 years old. What is the probability that 45 or more people in this sample have consumed alcoholic beverages? Answer is 0.0006
In conclusion, the probability that 45 or more people in a sample of fifty 18-20 year olds have consumed alcoholic beverages is 0.0006. This can be calculated by using the binomial distribution formula or by visually representing the data in a probability tree diagram.
The probability that 45 or more people in a sample of fifty 18-20 year olds have consumed alcoholic beverages is 0.0006. This can be determined by using the binomial distribution formula. The formula states that the probability of getting x successes in n trials is equal to nCr x (p)x (1-p)n-x, where n is the number of trials (in this case, 50), p is the probability of success (69.7%), and x is the number of successes (45). By plugging these values into the formula, we obtain a probability of 0.0006.
In addition to the binomial distribution formula, we can also use a visual representation such as a probability tree diagram to represent the given data. The probability tree diagram can be used to show the number of ways a certain outcome can occur. In this case, it would be the probability of 45 or more people in the sample of fifty 18-20 year olds consuming alcoholic beverages. The probability tree diagram consists of a trunk which branches off into multiple possible outcomes. At the end of each branch, there is a probability that corresponds to the probability of the given outcome occurring.
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q1.2 (3pts) an automated weight monitor can detect underfilled cans of beverages with probability 0.98. what is the probability it fails to detect an underfilled can for the first time when it encounters the 10th underfilled can?
The probability that it will fail to detect an underfilled can for the first time when it encounters the 10th underfilled can is approximately 0.005.
Since the probability that an automated weight monitor detects underfilled cans of beverages is 0.98, the probability that it will not detect an underfilled can for the first time when it encounters the 10th underfilled can is given by:
(1 - 0.98)10-1(0.98)
Using the formula above, we will solve for the probability below:
(1 - 0.98)10-1(0.98)≈0.005
Thus, the probability that it will fail to detect an underfilled can for the first time when it encounters the 10th underfilled can is approximately 0.005.
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Find the slope of the tangent line to the ellipse x^(2)/16 +y^(2)/4=1 at the point (x,y). slope =?
Are there any points where the slope is not defined? (Enter them as comma-separated ordered-pairs, e.g., (1,3), (-2,5). Enter none if there are no such points.) slope is undefined at ?
The slope of the tangent line at the point (x,y) is -x/(2y). The ellipse's slope is not defined at the coordinates (4, 0), (-4, 0).
What is slope of a tangent?The rate of change of a curve at a certain position is represented by the slope of a tangent line to the curve at that location. In other words, it indicates whether the curve is steep or shallow at that particular location. Calculating the derivative of a function in calculus also requires estimating the slope of a tangent line, which is a crucial step. We may determine the slope of the tangent line and subsequently the derivative of the function at a location by determining the limit of the slope of a secant line as the two points on the line approach closer and closer together.
The equation of the ellipse is x²)/16 +y²/4=1.
We take the derivative of the equation with respect to xto find the slope:
x²/16 + y²/4 = 1
(x²/16)' + (y²/4)' = 1'
2x/16 + 2y/4 * dy/dx = 0
dy/dx = -x/(2y)
When the denominator of 2y equals 0, there are some locations where the slope is not specified. The ellipse's slope is not defined at the coordinates (4, 0), (-4, 0), and all locations on the x-axis between these two points when y = 0, which occurs.
Hence, the slope of the tangent line at the point (x,y) is -x/(2y). The ellipse's slope is not defined at the coordinates (4, 0), (-4, 0).
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the city cafe is known for their vegetable plate lunch special that comes with four vegetables, cornbread, and sweet tea. if the four vegetables can be selected from a list of ten vegetables, what formula should be used to determine how many different vegetable plates are there? assume no vegetable is selected more than once
From the given list of vegetables, the number of different ways in which these vegetables can be selected from a list of vegetables such that no vegetable is selected more than once given here by the formula of Combination, which is: [tex]^nC_k[/tex] = n!/[k!(n-k)!].
What is the formula for vegetable plates?The city café is known for its vegetable plate lunch special that comes with four vegetables, cornbread, and sweet tea. If the four vegetables can be selected from a list of ten vegetables, the formula to determine how many different vegetable plates there are would be a combination of 10 vegetables taken 4 at a time.
The number of different ways that four vegetables can be selected from a list of ten vegetables is given by the formula of Combination, which is:
[tex]^nC_k[/tex] = n!/[k!(n-k)!]
where, n = number of elements in the set = 10 vegetables
k = number of elements chosen = 4 vegetables
n - k = number of elements not chosen = 10 - 4 = 6 vegetables
Therefore, the number of different vegetable plates is:
[tex]^nC_k[/tex] = 10!/ [4!(10-4)!]
[tex]^nC_k[/tex] = (10×9×8×7)/ (4×3×2×1) = 210
Hence, there are 210 different vegetable plates.
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cos(-180").tan 8.cos 690 sin (8-180) cos² (6-90) (5)
cos(-180°) = -1
tan 8° = 0.1425
cos 690° = 0
sin (8-180°) = - sin 172° = - 0.9997
cos² (6-90°) = cos(-84°) = 0.4997
Therefore, the answer to the expression is -0.4997.
you have spent $2,500 on liquor for your bar. your bar sales have been $12,890. what is your cost of sales for liquor, expressed as a percentage?
The cost of sales for liquor, expressed as a percentage is 19.39%.
What is the cost of sales for liquor in percentage?To compute for the cost of sales for liquor, expressed as a percentage given that you have spent $2,500 on liquor for your bar and your bar sales have been $12,890, you can use the formula:
Cost of sales = (Cost of Goods Sold / Total Sales) × 100
where, Cost of Goods Sold (COGS) = Beginning Inventory + Purchases - Ending Inventory (or the total cost of goods sold during the period)
Total Sales = Gross sales - Sales discounts - Sales returns and allowances
Let's compute for the COGS first:
COGS = Beginning Inventory + Purchases - Ending Inventory
= $0 + $2,500 - $0
= $2,500
Total Sales = Gross sales - Sales discounts - Sales returns and allowances
= $12,890 - $0 - $0
= $12,890
Cost of sales is obtained as follows:
Cost of sales = (Cost of Goods Sold / Total Sales) × 100
= ($2,500 / $12,890) × 100
= 19.39%.
Therefore, the cost of sales for liquor, expressed as a percentage is 19.39%.
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guys help please very urgent photo below
Answer:
-8x^2 - 10x + 7
Step-by-step explanation:
2x^2 - 10x^2 = -8x^2
-5x - 5x = -10x
3 - (- 4) = 7
-8x^2 - 10x + 7
Hope this helps!
what is the surface area of the net of this square pyramid?
Answer:
64sq cm
Step-by-step explanation:
To find area of net of square pyramid, you have to find area of the 4 triangles and area of square bottom.
Triangle Area = 1/2bh (times 4 because there are 4 triangles.
Square Area = lw
TA= 4(1/2bh)
4(1/2*4*6)
4(1/2*24)
4(12)
TA= 48 sq cm
SA= lw
4*4
SA= 16 sq cm
48 sq cm + 16 sq cm = 64 sq cm
O is the centre of this circle.
What is the size of angle x?
Fully justify your answer.
Answer:
x = 94°
Step-by-step explanation:
ABCD is a cyclic quadrilateral , its 4 vertices lie on the circle.
the opposite angles of a cyclic quadrilateral sum to 180° , that is
x + 86° = 180° ( subtract 86° from both sides )
x = 94°
For her phone service, Leila pays a monthly fee of $27, and she spends an additional $0.06 per minute of use. The least she has been charged in a month is $102.90.
What are the possible numbers of minutes she has used her phone in a month?
Use m for the number of minutes, and solve your inequality for m.
Answer:
Step-by-step explanation:
First Of all, Say the N-word, Now if she said the N-word, shell be given 27 dollars,Now I need to do my Homework, if i made you laugh, mark me the Brainliest
GIVING BRAINLIEST! IF TWO OR MORE PEOPLE ANSWER!
Answer:
a. Goron 224
b. Smith 96
Fishman 256
Step-by-step explanation:
a. For Goron: 640 x 0.35 = 224
b. For Smith: 640 x 0.15 = 96
For Fishman: 640 x 0.40 = 256
Anita borrowed ₹6000 from a bank at 15% interest rate per annum. Find the interest and
amount to be paid at the end of 3 years.
Answer: The interest and amount to be paid at the end of 3 years is Rs.8700
Step-by-step explanation:
let P ,R, T be the Principle amount , Rate of interest and Time
Given that ,P= 6000rs
R= 15%
T=3 years
Interest= PRT÷ 100=6000rs×15r×3t÷100
=2700rs
value to be paid after 3 years = 6000rs+2700rs= 8700rs
NEED HELP
5. Find the value of the variables of t and s
In given triangle, the value of t is 3.75 and the value of s is 10.4.
What are the 3 sides of a triangle?In a right triangle, the hypotenuse is the longest side, a "opposite" side is the one across from a given angle, and a "adjacent" side is close to a given angle. We use unique terminology to describe the sides of right triangles.
We can set up the following ratios because the two triangles in the illustration are comparable to one another:
t / 5 = 6 / 8 (using the smaller triangle)
s / 13 = 8 / 10 (using the larger triangle)
Simplifying these ratios, we get:
t / 5 = 3 / 4
s / 13 = 4 / 5
We may cross-multiply and simplify to find t and s:
t = 5(3/4) = 15/4 = 3.75
s = 13(4/5) = 10.4
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The coordinates below represent points that were translated.Draw a line to connect the coordinates with the correct description and algebraic representation of the translation.
(x-11, y+14) = (-4-7, 7+7) = (-11,14) which matches the new coordinates T(-11,14).
The coordinates' meaning is unclear?In this sense, coordinates are the points where a grid system intersects. GPS coordinates are typically created by combining latitude and longitude. The distance of north and the south from the equator, which is 0 degrees iof north and south, is measured by lines of latitude.
COORDINATES DESCRIPTION ALGEBRAIC REPRESENTATION8. T (-4,7) 7 units right, 7 units up (x-11, y+14)
9. U (3,-4) 7 units left, 7 units up (x+7, y+7)
10. V (-2,-10) 7 units right, 7 units down (x+7, y-7)
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Francis has an unpaid balance of $480 on his credit card. The annual percentage rate is 12%. What is the finance charge on his next monthly statement?
Answer:
$4.80
Step-by-step explanation:
You want to know the finance charge on a balance of $480 if the APR is 12%.
Finance chargeThe monthly finance charge is the product of the monthly interest rate and the balance. The monthly interest rate is 1/12 of the annual rate.
finance charge = (1/12 · 12%) · $480 = 0.01 · $480 = $4.80
The finance charge on the next monthly statement is $4.80.
What is the scale factor of the following pair of similar polygons ?
The scale factor of the following pair of similar polygons after the dilation is 0.7
Calculating the scale factor of the similar polygonsGiven
The pair of similar polygons
From the pair of similar polygons, we have the following corresponding side lengths
Pre-image of the polygon = 30
Image of the polygon = 21
The scale factor of the similar polygons is then calculated as
Scale factor = 21/30
Evaluate the quotient
Scale factor = 0.7
Hence, the scale factor is 0.7
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To perform a certain type of blood analysis, lab technicians must perform two procedures. The first procedure requires either one or two separate steps, and the second procedure requires either one, two, or three steps. a. List the experimental outcomes associated with performing the blood analysis. (1), (2), (3), (1, 1), (1, 2), (1,3), (2, 1), (2, 2), (2,3) b. Let z denote the total number of steps required to do the complete analysis (both procedures). Show what value of random variable will assume for each of the experimental outcomes. (If an outcome does not occur, enter "0.) Experimental Outcomes Value of a (2) (3) (1,1) (1,2) (1,3) (2.1) (2, 2) (2.3) (3.1) (3,2) (3.3)
For the blood analysis, there are a total of twelve possible experimental outcomes. The value of random variable for each of the experimental outcome is zero.
Therefore it can be shown as:
a. The experimental outcomes associated with performing the blood analysis are:
List out all the possible outcomes that can occur during the blood analysis.
The outcomes are based on the number of steps required for each of the procedures, with the first procedure having either one or two steps, and the second procedure having either one, two, or three steps.
(1) - First procedure requires one step, second procedure requires one step
(2) - First procedure requires two steps, second procedure requires one step
(3) - First procedure requires two steps, second procedure requires two steps
(1,1) - First procedure requires one step, second procedure requires one step
(1,2) - First procedure requires one step, second procedure requires two steps
(1,3) - First procedure requires one step, second procedure requires three steps
(2,1) - First procedure requires two steps, second procedure requires one step
(2,2) - First procedure requires two steps, second procedure requires two steps
(2,3) - First procedure requires two steps, second procedure requires three steps
b. Let z denote the total number of steps required to do the complete analysis. The value of the random variable for each of the experimental outcomes is:
It defines the value of the random variable, z, which denotes the total number of steps required to complete the analysis. It then provides the value of z for each of the experimental outcomes. For instance, outcome (1) requires one step in the first procedure and one step in the second procedure, so the value of z is 1+1=2. Similarly, for outcome (2), the value of z is 2+1=3.
(1) - z = 1 + 1 = 2
(2) - z = 2 + 1 = 3
(3) - z = 2 + 2 = 4
(1,1) - z = 1 + 1 = 2
(1,2) - z = 1 + 2 = 3
(1,3) - z = 1 + 3 = 4
(2,1) - z = 2 + 1 = 3
(2,2) - z = 2 + 2 = 4
(2,3) - z = 2 + 3 = 5
(3,1) - z = 2 + 1 = 3
(3,2) - z = 2 + 2 = 4
(3,3) - z = 2 + 3 = 5
If an outcome does not occur, the value of the random variable is 0.This is because the outcome did not happen, and there was no analysis to perform.
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When used in a particular DVD player, the lifetime of a certain brand of battery is normally distributed with a mean value of 12 hours and a standard deviation of 0.8 hours. Suppose that two new batteries are independently selected and put into the player. The player ceases to function as soon as one of the batteries fails. (You may need to use a table.) in USE SALT (a) What is the probability that the DVD player functions for at least 10 hours? (Round your answer to four decimal places.) (b) What is the probability that the DVD player works for at most 13 hours? (Round your answer to four decimal places.) (c) Find a number ** such that only 15% of all DVD players will function without battery replacement for more than x* hours. (Round your answer to two decimal places.) x* = hr
In the following question, among the various parts to solve- a). DVD player functions for at least 10 hours is 0.0062. b)DVD player functions for at most 13 hours is 0.8944. c). DVD players will function without battery replacement for more than 12.83 hours.
(a) Probability that the DVD player functions for at least 10 hours. (Round your answer to four decimal places.)Given, mean (μ) = 12 hours and standard deviation (σ) = 0.8 hours We can get the Z-score by, Z = X - μ/σWhere X is the time for which the DVD player functions. Z = 10 - 12/0.8Z = -2.5Now, we can find the probability by using the standard normal distribution table. From the table, the probability corresponding to -2.5 is 0.0062. Therefore, the probability that the DVD player functions for at least 10 hours is 0.0062.
(b) Probability that the DVD player works for at most 13 hours. (Round your answer to four decimal places.)Z = X - μ/σWhere X is the time for which the DVD player functions. Z = 13 - 12/0.8Z = 1.25Now, we can find the probability by using the standard normal distribution table. From the table, the probability corresponding to 1.25 is 0.8944. Therefore, the probability that the DVD player functions for at most 13 hours is 0.8944.
(c) Find a number ** such that only 15% of all DVD players will function without battery replacement for more than x* hours. (Round your answer to two decimal places.)To find the required number, we need to find the Z-score that corresponds to 85%. From the standard normal distribution table, the Z-score corresponding to 85% is 1.0364. Therefore, the required number is = μ + ZσX = 12 + 1.0364 x 0.8X = 12.8291 ≈ 12.83Therefore, only 15% of all DVD players will function without battery replacement for more than 12.83 hours.
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1/sinx+cosx + 1/sinx-cosx = 2sinx/sin^4x-cos^4x
The simplified expression is 2cos²(x) + sinx - 1 = 0
The expression we will be simplifying is
=> 1/sinx+cosx + 1/sinx-cosx = 2sinx/sin⁴x-cos⁴x.
To begin, let us look at the left-hand side of the expression. We can combine the two fractions using a common denominator, which gives us:
(1/sinx+cosx)(sinx-cosx)/(sinx+cosx)(sinx-cosx) + (1/sinx-cosx)(sinx+cosx)/(sinx-cosx)(sinx+cosx)
Simplifying this expression using the distributive property, we get:
(1 - cosx/sinx)/(sin²ˣ - cos²ˣ) + (1 + cosx/sinx)/(sin²ˣ - cos²ˣ)
Next, we can simplify each fraction separately. For the first fraction, we can use the identity sin²ˣ - cos²ˣ = sinx+cosx x sinx-cosx to obtain:
1 - cosx/sinx = (sinx+cosx - cosx)/sinx = sinx/sinx = 1
Similarly, for the second fraction, we can use the same identity to obtain:
1 + cosx/sinx = (sinx-cosx + cosx)/sinx = sinx/sinx = 1
Substituting these values back into the original expression, we get:
1 + 1 = 2sinx/(sin⁴x - cos⁴x)
Now, we can simplify the denominator using the identity sin²ˣ + cos²ˣ = 1 and the difference of squares formula:
sin⁴x - cos⁴x = (sin²ˣ)² - (cos²ˣ)² = (sin²ˣ + cos²ˣ)(sin²ˣ - cos²ˣ) = sin²ˣ - cos²ˣ
Substituting this back into the expression, we get:
2 = 2sinx/(sin²ˣ - cos²ˣ)
Finally, we can simplify the denominator using the identity sin²ˣ - cos²ˣ = -cos(2x):
2 = -2sinx/cos(2x)
Multiplying both sides by -cos(2x), we get:
-2cos(2x) = 2sinx
Dividing both sides by 2, we get:
-cos(2x) = sinx
Using the double-angle formula for cosine, we get:
-2cos²(x) + 1 = sinx
Simplifying this expression, we get:
2cos²(x) + sinx - 1 = 0
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Show all steps and how you got the answer
Answer:
x = 8500
y = 15000
Step-by-step explanation:
small vans: x
large vans: y
A: 5x + 2y = 72500
B: 2x + 6y = 107000
5x + 2y = 72500 => y = (72500 - 5x)/2
2x + 6(72500 - 5x)/2 = 107000
2x + 217500 - 15x = 107000
15x - 2x = 217500 - 107000
13x = 110500
x = 110500/13 = 8500
y = (72500 - 5x)/2 = y = (72500 - 5x8500)/2 = 15000
Given the lengths of two sides of a triangle, write an equality to indicate between which two numbers the length of the third side must fall.
The sides are:
8 and 13
I will award brainliest to the first correct answer with a decent explanation
The length of the third side must fall between 8 and 13. This is because the sum of the lengths of any two sides of a triangle must always be greater than the length of the third side.
Suppose a tank of water is a cylinder. The tank has a diameter of 14 inches and is filled
to a height of 9 inches. A fish tank decoration is placed in the tank and the water rises
by 2 inches with the decoration being completely covered by water. Find the volume of
the decoration to the nearest tenth of a cubic inch.
The decoration's volume, to the closest tenth of an inch cubic, is: 308.9 cubic inches make up V.
what is volume ?The quantity of space that an object or substance occupies is measured by its volume. Usually, it is expressed in cubic measures like cubic metres, cubic feet, or cubic inches. By multiplying an object's length, width, and height, or by applying a formula unique to the shape of the object, one can determine the volume of the object.
given
The cylinder's radius is equal to half of its diameter, or 14/2, or 7 inches. The new water level is 9 + 2 = 11 inches because the initial water level was 9 inches and the decoration raised the water level by 2 inches.
The decoration's volume is equivalent to the volume of water it removed from the area.
We can determine the volume of the ornamentation by using the following formula: V = r2h.
V = (72/2), which equals 98 cubic inches.
The decoration's volume, to the closest tenth of an inch cubic, is: 308.9 cubic inches make up V.
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